Updated: 2020-12-09 06:29:57 PDT

Original version created 2020-05-03. See below for revision history

Intro


The spread of the SARS-COV-19 viral disease defies description in terms of a single statistic. To be informed about personal risk we need to know more than how many people have been sick at a national level or even state level, we need information about how many people are currently sick in our communicty and how the number of sick people is changing is changing at a state and even county level. It can be hard to find this information.

This analysis seeks to fill partially that gap. It includes:
1. Several national pictures of disease trends to enable a “large pattern” view of how disease has and is evolving a on country-wide scale.
2. A per capita analysis of disease spread.
3. A more granular analysis of regions, states, and counties to shed light on local disease pattern evolution.
4. Details of the time evolution of growth statistics.


This computed document is part of a constantly evolving analysis, so please “refresh” for the latest updates. If you have suggestions or comments please reach out on twitter @WinstonOnData or facebook.


You are welcome to visit my code repository on Github.
You are also welcome to visit my analysis on the Politics of COVID
Finally, you can alway check my Rpubs for new documents and updates.

National Statistics

Total & Active Cases, and Deaths

These trend charts show the national disease statistics. Note that raw daily trends are systematically related to the M-F work week.

Mortality and \(R_e\)

Distribution of \(R_e\) Values

There is a wide distribution of \(R_e\) across regions and counties. The distributions in the graph below looks roughly symmetrical because the x-scale is logarithmic.

National Maps

State Level Data

There are several maps below. These include:

  • pandemic total cases (How many people have been sick?)
  • pandemic total cases per capita (What fraction of people have been sick?)
  • daily cases per capita (what fraction of people are getting sick?)
  • forecast short term cases per capita (based on \(R_e\)) (how fast is the disease growning or shrinking?)

Pandemic Totals

Current Status of Active Disease

Computed Reproduction Rate \(R_e\).

County Data

While the State-Level Data tell as remarkable story, outbreaks tend to be highly localized to communities - therefor it’s informative to look at County-level data


state R_e cases daily cases daily cases per 100k
Indiana 1.12 397062 7103 107.0
Ohio 1.26 501586 11907 102.3
Utah 1.06 220445 3017 99.1
Minnesota 0.96 360608 5444 98.5
Nevada 1.14 174038 2808 96.1
South Dakota 0.91 85658 785 92.4
Nebraska 0.98 143186 1752 92.0
Idaho 1.11 114145 1540 91.2
Wyoming 0.95 37519 512 88.0
Arizona 1.17 376834 6058 87.2
Delaware 1.24 41349 812 85.5
Colorado 1.04 271348 4684 84.7
Montana 1.02 69594 871 83.6
Pennsylvania 1.22 443257 10432 81.6
Kansas 1.03 178361 2353 80.9
Oklahoma 1.07 221440 3155 80.5
Connecticut 1.28 136218 2867 80.1
Tennessee 1.08 403848 5178 77.9
Wisconsin 0.99 448903 4371 75.6
Kentucky 1.02 211048 3323 74.8
New Mexico 0.89 111060 1561 74.6
Michigan 1.01 441725 7359 73.9
Illinois 1.01 807556 9412 73.4
West Virginia 1.17 57267 1286 70.3
Alabama 1.13 276513 3362 69.1
California 1.32 1422436 26931 68.8
Arkansas 1.08 171914 2047 68.4
Massachusetts 1.22 254190 4674 68.4
North Dakota 0.78 83774 484 64.3
Missouri 1.08 317258 3862 63.4
Mississippi 1.07 168353 1866 62.4
Iowa 0.91 247766 1942 62.0
New Jersey 1.14 378166 5262 59.2
New Hampshire 1.27 26046 773 57.5
South Carolina 1.31 236946 2769 55.9
North Carolina 1.19 404675 5388 53.1
New York 1.17 729025 10165 51.8
Louisiana 1.02 254662 2362 50.6
Texas 1.07 1372971 13607 48.8
Maryland 1.15 220495 2863 47.7
Georgia 1.18 490547 4806 46.7
Florida 1.07 1072903 9545 46.3
Virginia 1.28 207040 2936 42.2
Washington 1.15 193736 3019 41.4
Oregon 1.07 87395 1556 38.1
Rhode Island 0.43 52468 300 28.4
Maine 1.32 14030 324 24.3
Vermont 1.16 5222 130 20.8

Regional Snapshots

Regional snapshots reveal the highly nuanced behavior of disease spread. Each snaphot includes multiple states and selected counties.

How to read the charts

There are four components:
1. State Maps show the number of active cases and with the Reproduction rate encoded as color.
2. State Graphs State-wide trend graphs.
3. Severity Ranking These is a table of counties where the highest number of new cases are expected. Severity is a compounded function \(f(R, cases(t))\). This is useful for finding new (often unexpected) “hot spots.” Added per capita rates.
4. County Graphs encode the R-value in the active number of cases. R is the Reproduction Rate.

(NOTE: R < 1 implies a shrinking number of active cases, R > 1 implies a growing number of active cases. For R = 1, active cases are stable. ).


Washington and Oregon

California

Four Corners

Mid-Atlantic

Deep South

FL and GA

Texas & Oklahoma

Michigan & Wisconsin

Minnesota, North Dakota, and South Dakota

Connecticut, Massachusetts, and Rhode Island

New York

Vermont, New Hampshire, and Maine

Carolinas

North-Rockies

Midwest

Tennessee and Kentucky

Missouri and Arkansas

Conclusions

It’s in control some places, but not all places. And many places are completely out-of-control.

Stay Safe!
Be Diligent!
…and PLEASE WEAR A MASK



Built with R Version 4.0.3
This document took 619.2 seconds to compute.
2020-12-09 06:40:16

version history

Today is 2020-12-09.
203 days ago: plots of multiple states.
195 days ago: include \(R_e\) computation.
192 days ago: created color coding for \(R_e\) plots.
187 days ago: reduced \(t_d\) from 14 to 12 days. 14 was the upper range of what most people are using. Wanted slightly higher bandwidth.
187 days ago: “persistence” time evolution.
180 days ago: “In control” mapping.
180 days ago: “Severity” tables to county analysis. Severity is computed from the number of new cases expected at current \(R_e\) for 6 days in the future. It does not trend \(R_e\), which could be a future enhancement.
172 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
167 days ago: Added Per Capita US Map.
165 days ago: Deprecated national map. can be found here.
161 days ago: added state “Hot 10” analysis.
156 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
154 days ago: added per capita disease and mortality to state-level analysis.
142 days ago: changed to county boundaries on national map for per capita disease.
137 days ago: corrected factor of two error in death trend data.
133 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
128 days ago: added county level “baseline control” and \(R_e\) maps.
124 days ago: fixed normalization error on total disease stats plot.
117 days ago: Corrected some text matching in generating county level plots of \(R_e\).
111 days ago: adapted knot spacing for spline.
97 days ago:using separate knot spacing for spline fits of deaths and cases.
95 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
67 days ago: improved national trends with per capita analysis.
66 days ago: added county level per capita daily cases map. testing new color scheme.
39 days ago: changed to daily mortaility tracking from ratio of overall totals.
32 days ago: added trend line to state charts.
4 days ago: decreased max value of Daily Cases per 100k State map.

Appendix: Methods

Disease data are sourced from the NYTimes Github Repo. Population data are sourced from the US Census census.gov

Case growth is assumed to follow a linear-partial differential equation. This type of model is useful in populations where there is still very low immunity and high susceptibility.

\[\frac{\partial}{\partial t} cases(t, t_d) = a \times cases(t, t_d) \] \(cases(t)\) is the number of active cases at \(t\) dependent on recent history, \(t_d\). The constant \(a\) and has units of \(time^{-1}\) and is typically computed on a daily basis

Solution results are often expressed in terms of the Effective Reproduction Rate \(R_e\), where \[a \space = \space ln(R_e).\]

\(R_e\) has a simple interpretation; when \(R_e \space > \space 1\) the number of \(cases(t)\) increases (exponentially) while when \(R_e \space < \space 1\) the number of \(cases(t)\) decreases.

Practically, computing \(a\) can be extremely complicated, depending on how functionally it is related to history \(t_d\). And guessing functional forms can be as much art as science. To avoid that, let’s keep things simple…

Assuming a straight-forward flat time of latent infection \(t_d\) = 12 days, with \[f(t) = \int_{t - t_d}^{t}cases(t')\; dt' ,\] \(R_e\) reduces to a simple computation

\[R_e(t) = \frac{cases(t)}{\int_{t - t_d}^{t}cases(t')\; dt'} \times t_d .\]

Typical range of \(t_d\) range \(7 \geq t_d \geq 14\). The only other numerical treatment is, in order to reduce noise the data, I smooth case data with a reticulated spline to compute derivatives.


DISCLAIMER: Results are for entertainment purposes only. Please consult local authorities for official data and forecasts.